Parallel Inductors Calculator — Equivalent Inductance of Coils in Parallel

Background.

Inductors in parallel combine the way resistors in parallel do: the reciprocals add, and the equivalent is always smaller than the smallest branch. Put a 6 mH, a 12 mH and a 24 mH coil across the same two nodes and you get 24/7 mH, about 3.43 mH. For exactly two coils the product-over-sum shortcut is quicker by hand — 6 mH with 12 mH gives (6 × 12)/(6 + 12) = 4 mH.

The reason is what parallel branches share. They all sit at the same voltage, and for an inductor the rate of change of current is v/L, so a small inductance changes its current fastest. The branch currents add, which makes the reciprocals add. That also produces the practical warning this page prints beside the result: the branches do not share the current equally. The smallest inductance takes the largest share and saturates first, so paralleling coils to increase current handling only works if the coils are matched.

As with the series case, this is the uncoupled answer. Coils that share a core or link flux follow L_eq = (L₁L₂ − M²)/(L₁ + L₂ ∓ 2M) instead, where M is the mutual inductance. This page does not ask for a coupling coefficient and so cannot compute that — the familiar L/2 shortcut for two identical coils in parallel holds only when they are magnetically isolated.

What is parallel inductors calculator?

A parallel connection puts every inductor between the same two nodes, so all of them see the same voltage v. Rearranging the element law v = L di/dt gives di/dt = v/L for each branch, and because the branch currents add, the total rate of change is v times the sum of the reciprocals. Comparing that with di/dt = v/L_eq for a single equivalent inductor gives 1/L_eq = Σ(1/Lᵢ). Inverting produces the equivalent inductance, and for exactly two branches the same thing can be written as the product over the sum. Two consequences matter in practice. The equivalent is always below the smallest branch, because adding another reciprocal can only increase the reciprocal sum — which is the arithmetic check that catches a mis-applied series formula. And current divides inversely with inductance rather than evenly, so the smallest coil carries the largest share and reaches saturation first. The rule assumes the coils are magnetically isolated; where flux links between them, the mutual inductance term enters and the reciprocal rule no longer applies.

How to use this calculator.

1. 01Type the inductor values into the list box, separated by commas, spaces or new lines. Two to twenty values are accepted.
2. 02Choose the unit that applies to every value in the list — convert first if the branches mix scales.
3. 03Read the equivalent inductance, then check it against the smallest-inductor figure. A parallel equivalent must be below it.
4. 04For two coils, verify by hand with the product-over-sum shortcut: (L₁ × L₂) ÷ (L₁ + L₂).
5. 05If you are paralleling coils to carry more current, match them — the smallest inductance takes the largest share and saturates first.
6. 06If any two coils share a core or sit close together, this figure does not apply; use the coupled formula with the mutual inductance.

The formula.

Convert every entered value to henries, then add the reciprocals and invert. With 6, 12 and 24 in millihenries the reciprocals are 1/6, 1/12 and 1/24 per millihenry, which over a common denominator of 24 is 4/24 + 2/24 + 1/24 = 7/24. Inverting gives 24/7 = 3.4285714286 mH, or 3428.5714285714 µH. Note the result is below the smallest branch, the 6 mH, as every parallel combination must be.

For exactly two coils there is a shortcut worth knowing, and Fiore's own worked example uses it: L_eq = (L₁ × L₂) ÷ (L₁ + L₂). For 6 mH and 12 mH that is 72 ÷ 18 = 4 mH. The shortcut and the reciprocal method agree exactly — this page uses the reciprocal form because it generalises to any number of branches, and a test asserts the two agree across several pairs.

The derivation takes one line. Parallel branches share a voltage v. For each inductor, di/dt = v/L. The branch currents add, so the total rate of change is v Σ(1/Lᵢ). Comparing with di/dt = v/L_eq gives 1/L_eq = Σ(1/Lᵢ).

That same relation explains the current division, and it runs the opposite way to most people's intuition. Since di/dt = v/L with v common, the smallest inductance ramps its current fastest and ends up carrying the largest share. Paralleling a 10 µH choke with a 100 µH one does not halve the current in each; the 10 µH branch takes roughly ten times the current of the other and saturates long before it. Only matched coils divide current evenly.

What the reciprocal rule leaves out is mutual inductance. Coupled coils in parallel follow L_eq = (L₁L₂ − M²)/(L₁ + L₂ ∓ 2M), which this page does not compute because it does not ask for M or a coupling coefficient. The familiar L/2 for two identical parallel coils is only true when they are magnetically isolated.

Rounding happens once, at the end, to ten decimal places, with intermediate arithmetic at forty significant digits so a twenty-branch reciprocal sum does not accumulate error. Outputs are in millihenries and microhenries rather than henries because nanohenry-scale results in henries would round away at that precision.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Engineering LibreTexts / James M. Fiore, Introduction to Circuit Analysis, §6.2.2 'Inductance and Inductors'. Primary source for the rule implemented here: 'inductors in parallel behave like resistors in parallel. The equivalent of parallel inductors can be found by using either the product-sum rule or by taking the reciprocal of the sum of their reciprocals.' Its Example 9.2.1 combines 6 mH and 12 mH via L_parallel = (L₂ × L₃)/(L₂ + L₃) for 4 mH, which this calculator reproduces exactly. Retrieved 2026-07-29.
2. [2]OpenStax (Rice University), University Physics Volume 2, §14.2 'Self-Inductance and Inductors'. Independent second authority for the element law the derivation rests on — ε = −L(dI/dt), one henry being one volt-second per ampere. It is di/dt = v/L applied to each branch at a shared voltage that makes the reciprocals add. Retrieved 2026-07-29.
3. [3]MIT OpenCourseWare, 6.002 Circuits and Electronics, Spring 2007 (Prof. Anant Agarwal). Course materials on the inductor element law and the series/parallel reduction of energy-storage elements. Landing page verified to load and to list the course number, term and instructor. Retrieved 2026-07-29.